Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024
Disaggregation of revenue by major customer markets
Net sales	$ 678.2	$ 567.3	$ 2,026.0	$ 1,662.4
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	270.7	242.3	794.1	706.7
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	220.9	200.2	652.1	595.6
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	49.8	42.1	142.0	111.1
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	215.9	140.8	662.3	423.7
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	193.6	128.2	591.5	380.7
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	22.3	12.6	70.8	43.0
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	162.9	165.5	495.2	478.4
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	69.4	69.1	211.4	195.3
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	93.5	96.4	283.8	283.1
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	28.7	18.7	74.4	53.6
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.6	1.7	3.6	5.3
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	27.1	17.0	70.8	48.3
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	678.2	567.3	2,026.0	1,662.4
Aviation Services | U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	494.8	422.2	1,468.6	1,236.5
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	98.7	90.4	316.3	263.6
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	75.0	47.5	204.6	133.6
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	$ 9.7	$ 7.2	$ 36.5	$ 28.7